{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logic of `gradient boosting` is very simple (if explained intuitively, without using mathematical notation). I expect that whoever is reading this would have done `simple linear regression modeling`. \n",
    "\n",
    "One of the very basic assumption of linear regression is that it's sum of residuals is 0. Although, tree based models are not based on any of such assumptions, but if we think logic (not statistics) behind these assumptions, we might argue that, if sum of residuals is not 0, then most probably there is some pattern in the residuals of our model which can be leveraged to make our model better. \n",
    "\n",
    "So, the intuition behind `gradient boosting` algorithm is to leverage the pattern in residuals and strenghten a weak prediction model, until our residuals become randomly (maybe random normal too) distributed. Once we reach a stage that residuals do not have any pattern that can be modeled, we can stop modeling residuals (as it might lead to overfitting). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from fastai.imports import *\n",
    "from IPython.display import display\n",
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "metadata": {},
   "outputs": [],
   "source": [
    "def std_agg(cnt, s1, s2): return math.sqrt((s2/cnt) - (s1/cnt)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 479,
   "metadata": {},
   "outputs": [],
   "source": [
    "class DecisionTree():\n",
    "    def __init__(self, x, y, idxs = None, min_leaf=2):\n",
    "        if idxs is None: idxs=np.arange(len(y))\n",
    "        self.x,self.y,self.idxs,self.min_leaf = x,y,idxs,min_leaf\n",
    "        self.n,self.c = len(idxs), x.shape[1]\n",
    "        self.val = np.mean(y[idxs])\n",
    "        self.score = float('inf')\n",
    "        self.find_varsplit()\n",
    "        \n",
    "    def find_varsplit(self):\n",
    "        for i in range(self.c): self.find_better_split(i)\n",
    "        if self.score == float('inf'): return\n",
    "        x = self.split_col\n",
    "        lhs = np.nonzero(x<=self.split)[0]\n",
    "        rhs = np.nonzero(x>self.split)[0]\n",
    "        self.lhs = DecisionTree(self.x, self.y, self.idxs[lhs])\n",
    "        self.rhs = DecisionTree(self.x, self.y, self.idxs[rhs])\n",
    "\n",
    "    def find_better_split(self, var_idx):\n",
    "        x,y = self.x.values[self.idxs,var_idx], self.y[self.idxs]\n",
    "        sort_idx = np.argsort(x)\n",
    "        sort_y,sort_x = y[sort_idx], x[sort_idx]\n",
    "        rhs_cnt,rhs_sum,rhs_sum2 = self.n, sort_y.sum(), (sort_y**2).sum()\n",
    "        lhs_cnt,lhs_sum,lhs_sum2 = 0,0.,0.\n",
    "\n",
    "        for i in range(0,self.n-self.min_leaf-1):\n",
    "            xi,yi = sort_x[i],sort_y[i]\n",
    "            lhs_cnt += 1; rhs_cnt -= 1\n",
    "            lhs_sum += yi; rhs_sum -= yi\n",
    "            lhs_sum2 += yi**2; rhs_sum2 -= yi**2\n",
    "            if i<self.min_leaf or xi==sort_x[i+1]:\n",
    "                continue\n",
    "\n",
    "            lhs_std = std_agg(lhs_cnt, lhs_sum, lhs_sum2)\n",
    "            rhs_std = std_agg(rhs_cnt, rhs_sum, rhs_sum2)\n",
    "            curr_score = lhs_std*lhs_cnt + rhs_std*rhs_cnt\n",
    "            if curr_score<self.score: \n",
    "                self.var_idx,self.score,self.split = var_idx,curr_score,xi\n",
    "\n",
    "    @property\n",
    "    def split_name(self): return self.x.columns[self.var_idx]\n",
    "    \n",
    "    @property\n",
    "    def split_col(self): return self.x.values[self.idxs,self.var_idx]\n",
    "\n",
    "    @property\n",
    "    def is_leaf(self): return self.score == float('inf')\n",
    "    \n",
    "    def __repr__(self):\n",
    "        s = f'n: {self.n}; val:{self.val}'\n",
    "        if not self.is_leaf:\n",
    "            s += f'; score:{self.score}; split:{self.split}; var:{self.split_name}'\n",
    "        return s\n",
    "\n",
    "    def predict(self, x):\n",
    "        return np.array([self.predict_row(xi) for xi in x])\n",
    "\n",
    "    def predict_row(self, xi):\n",
    "        if self.is_leaf: return self.val\n",
    "        t = self.lhs if xi[self.var_idx]<=self.split else self.rhs\n",
    "        return t.predict_row(xi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(0,50)\n",
    "x = pd.DataFrame({'x':x})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 427,
   "metadata": {},
   "outputs": [],
   "source": [
    "# just random uniform distributions in differnt range\n",
    "\n",
    "y1 = np.random.uniform(10,15,10)\n",
    "y2 = np.random.uniform(20,25,10)\n",
    "y3 = np.random.uniform(0,5,10)\n",
    "y4 = np.random.uniform(30,32,10)\n",
    "y5 = np.random.uniform(13,17,10)\n",
    "\n",
    "y = np.concatenate((y1,y2,y3,y4,y5))\n",
    "y = y[:,None]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scatter plot of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 428,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((50, 1), (50, 1))"
      ]
     },
     "execution_count": 428,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Cui5tH237Nts7bD9g+7x8+6G2b7H9YP79kKJqQHc2bRvR8g1bdOy6b2n5hi2zngJQRUwK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2d82de80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,5))\n",
    "plt.plot(x,y, 'o')\n",
    "plt.title(\"Scatter plot of x vs. y\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Boosting (DecisionTrees in a loop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/groverprince/anaconda/envs/fastai/lib/python3.6/site-packages/matplotlib/pyplot.py:523: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).\n",
      "  max_open_warning, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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NbepRNc3FgFTndd/Wfenb2rfb68fFFLedZmtmm28btLwRf8/VyLRGwsyah1jl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\niIiIiIikpkRCRERERERS+//E/ks9zW//lwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2d34da90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cstI8tDk2Lo2pEMlGUYmEu59Q6Hkzm+LuaU65dwswBZgVfv99ivsWEZEqYGY/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\nIiIiIpLY/wdTGPsIaYrHZgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f4ef630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KUc5Kqd4T9TyISL1z909nXYZ6F9dTEdf4nzlhZslehyljp5Tdm6AxFSLZKSuQ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\nAwHw8kA+8mDMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c30316710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ERERERCQxJRIiIiIiIpKYEgkREREREUlMiYSIiIiIiCSmREJERERERBLLdEE6qR/zlnYw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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f1ea048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SE9e60efeNMeQitNOg6VLYfv2tCOpvUJLgpIEyQkzOy78fTJB96K14c/oZluf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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f3820b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MmvrZZXXM9kuB43ptWwDc7O4HADeHr+subj2EoTgkJ65344XOLvUYVDNlCowb\nV4y8hAKvkSDF5u4/Bt4GXBf+O2IoTpQhIpI3tfYkPGRmPwV+7O5/7v2mu38y6ofc/bdmNqnX5lOA\nd4TfLwNuA/6lxnLUrJFmDKnW66EegyrMgt6E1XExao60t8PkyVmXQmTQmNkb3P2B8no8wJPh1/Fm\nNr6R1ucREWlEtQYJBwMfAH5kZsOAS4Cr3P0vAzjn3u7+NIC7P21mew3gGDVplAa25knfCUceCStW\nwMaNsFdqv0rZa28PrlWkOP4ZmAd8K+K9hlufR0Sk0dS6TsIW4IfAD83sbwhWXv522LvwVXd/KI3C\nmdk8gkqCCRMmpHGKIaGRej2GnHJewh13wOzZ2ZYlLV1d8NxzGm4kheLu88Kv/S6EUpS6QkRkMNWc\nk2BmJ5vZdcCFBE92JgM3ACsTnvMZM9snPO4+wMa4Hd19qbvPcPcZ48aNS3iaxjJ7eiurFxzNo4tP\nZPWCoxUg1OrNb4YRI/Kdl/Dss+CuIEEKycxOM7Pdwu+/aGbLzWx65T5FqisGw+XrLmfSBZMY9uVh\nTLpgEpevuzzrIolIBmqdAvVBglyCJe4+3d3Pd/dn3P2nwC8TnvN6YG74/VzgZwl/XmSHkSPhsMPy\nnZegNRKk2P7V3beY2VHALIJctu9nXKbcunzd5cy7YR6Pv/A4jvP4C48z74Z5dQ0UFISINIZag4SD\n3f1Md+/zuNbdPxX3Q2Z2JfDfwFQze8rMziSYzu7dZvYg8O7wtcjAzZwJd90FL7+cdUnSoSBBiq2c\nrHUi8B/u/jNgRIblybUv3PwFtnZt7bFta9dWvnDzF+rSuB+MIERE6qOmIMHdXxzIwd39dHffx92b\n3X1fd7/Y3Te5+zHufkD4dfNAji3yqiOPhFdegTVrsi5JOhQkSLG1mdkPgPcBK81sF+q3EKj08sQL\nT0RuLzfmd7ZxXy0IEZGhRTdaaXzlWX/ympdQDhL23jvbcohk433AKuA4d+8AxgDzsy1Sfk0YHZ34\n3WRNiRv3UT0PcUFI3HYRyU7V2Y3M7Ajg9+7ug1QekeT23jtYWO3ii+HRR7MuTf3dcQeMHg2l+q0W\nLtIo3H2rmW0EjiLIj9sWfpUULDxmIfNumNcjIBjVPKpPgFAW17gvDysq/1y552FMaQybOjf12T8u\nOBGR7PQ3Bepc4CIz+1+CBOVfunt7+sUSSehDH4LvfheuuSbrkqTjhBOyLoFIJszsXGAGMBX4MdAM\n/BcwM8ty5dWcaXOAYFjQEy88wYTRE1h4zEK+cPMXePyFx/vsH9e4jxtWVBpe6hN0jGoexcJjFsaW\n6fJ1l/cpT7mcIpKeqkGCu//K2QGEAAARRklEQVQ/CFa+BI4HLjWz0cCtBEHDanfvrnIIkcHxpS8F\n/0Qkb/4vMB24G8DdN5SnRJV0zJk2J7IRHtXDENe4j+th2Ny5mctOvazmRn9cj0S5nCKSnloXU3sA\neIBgAbUS8E7gNOB8gic8IiIiaXjF3d3MHMDMXpN1gYoorochrqE+YfSE2J6HuCAkSrVEZwUJIumq\nKUio5O6dBAuoJV1ETUREJKlrwtmNWszsY8BHgR9lXKZCStK4j8ttqDasKIoSnUWyo9mNRERkyHL3\nfwN+ClxLkJfwJXf/Tralkv7MmTaHpSctZeLoiRjGxNETWXrS0qpBRtRsSHE5D/0lOmvBNpGdl7gn\nQUREZDC5+03ATQBm1mRmc9xdrb4hIi6xOEnPQ1zuwdxD5rLs3mWJE52VxyCy82rqSTCzT5rZHmkX\nRkREBMDMdjezc8zs383sWAt8EniEYO0EGQLqtYJyXO7BygdXJu6R0IJtIvVRa0/Ca4E7zexu4BJg\nldZOEBGRFF0GPA/8N/D3BAuojQBOcfd7siyY7FCvxOJquQdJeiT6O5aI1K7W2Y2+aGb/ChwLfAT4\ndzO7BrjY3R9Os4AiRbBibRtLVq1nQ0cn41tKzJ81ldnTW7MulkiWJrv7NAAz+xHwHDDB3bdkWyyp\nVK8GebXZkKqJGuo00GOJSE81Jy6HPQft4b9twB7AT83smymVTaQmK9a2MXPxLey/4EZmLr6FFWvb\nBrQ9KyvWtnHO8nW0dXTiQFtHJ+csX5d5uUQy1lX+JlyP51EFCPVVj+TegSYW97bwmIWMah7VY1ut\nuQe9hzqdcMAJiY8lIn3VmpPwKTNbA3wTWA1Mc/d/AA4D/jbF8olUFdfA/uKKdYm2Z9kgX7JqPZ1d\nPdck7OzqZsmq9RmVSGRIOMTM/hL+2wIcXP7ezP6SdeEaXb1yCQbSuI8ykNmQ6pnHIAOnmaTyy2pJ\nLTCzrxAMLerTf2dmb3T3+9MoXKUZM2b4XXfdlfZppMHMXHwLbR2dfbY3mdEd8bsdt721pcTqBUen\nUsb+7L/gRqL+Cg14dPGJg10caVBmtsbdC7+4peqK2ky6YFLkkJyJoyfy2NmPJTpW3OxGaRv25WF4\nxN3TMLafuz3180vfmaQgCBIVlA1ttdYXNfUkuPuXogKE8L3UAwSROBsiAgQgMhCotj3uOINhfEsp\n0XYRkZ1Vz+TeOdPm8NjZj7H93O08dvZjg9Y4rNdQJ6lNVI9B1jNJqRcjXVpMTRpaXEO6ySzR9no3\nyJPkQ8yfNZVSc1OPny81NzF/1tS6lklEpCwPDex6DXWS/sUNT4vqjYLBmUmqXkPmJJ6CBGlocQ3s\n09+2X6Lt9WyQJ82TAFh06jRaW0oYwdCnRadO0+xGIpKaPDSwB5LHIAMT12PQZE2R+5eDzXo96Vcv\nRjZqykkYCjTOVOLETR+adHu9JM2TyDIfQvJDOQkB1RW1yyqXQAZX3P9zku1nLD8jMv8DguAyKicB\niM1XAGo+d9xxegcIZYORk9LouRi11hcKEkTqLC4ROY4SlKUeFCQEVFeI7BDXmJ17yFyW3bus5u2l\n4SU2dW7qc/yJoyey8JiFkQ3+uOT4saWxdG7r3OlzN1kT3d7dZ/tAku+TqmfifxZqrS9qXXFZRGo0\nvqWUqCehWj6EFlkTEZGBihuSs3TN0j4N7GrbS8NLkT0G5YAg6ul5XF5CVIO/2rnjegy6vTu2THHq\n1XtWlFW9lZMgUmdJ8yTi8iG0yJqIiOyMuEZr1BP4ats3d25OnP+RNAk+7txxymWotUz1THTOQ+J/\nLRQkiNTZ7OmtkYnIX5s9LVGCshZZExGRnRHXaI1LOK6WiJx0qtu45PixpbGJzj22NDY2yT5JmeqZ\n6JyHxP9aZBYkmNlxZrbezB4yswVZlUOkFkmmNIUgUFi94GgeXXwiqxcc/WogELc9StzaDVmu6SAi\nIo0jrjE777B5ibYPpPEbN/vUhcdfmOjcFx5/YV1msar32iBJy5R0NqShMHtSJjkJZtYEXAS8G3gK\nuNPMrnf3P2dRHhGoPkvSOcvXvfpUvzzs567HN3PtmrY+24G65A3E5TZokTUREalFudEaNQ5/5oSZ\nibYP9PxxP5v03Ds7a9CE0RMik40HOkSo2rX11juBvDzUqXycnd0/LZnMbmRmRwDnufus8PU5AO6+\nKO5nNGOFpKl3IABBvsCiU6exZNX6TKY0rVYmJS9Lb5rdKKC6QkSSTKVabUrWekk6G1LasyfVWl9k\nNdyoFXiy4vVT4TaRTFQb/x83vCcqQID6DQeKy21QgCAiIhItLkEZiBwiBMQmNNdryE/SoU5DZfak\nrKZAtYhtfVpcZjYPmAcwYUK+MsZlaKk2/r+eU5omNXt6q4ICkX6orhCRsmoJylHJzZMumBS5/1m/\nOKvHeg61DvmJ6sWoNtSpHvunNQQpq56Ep4D9Kl7vC2zovZO7L3X3Ge4+Y9y4cYNWOCmeuIZ9OTeh\nHlOaikg6VFeISFm9ns5v6tyUeDakuF6MEw44ITIp+4QDTqjL/mklNWcVJNwJHGBm+5vZCOADwPUZ\nlUUkNhAoJy/XY0pTERERSVfSNQySJi5XG/IT14ux8sGVkUOdVj64si77D2Qa11pkkrgMYGYnABcA\nTcAl7l51fi0lo0natLqxNDIlLgcGq66oV5f/YA4dECmC3jMDwY4E5VpmEirvXxpeilwdulry8LAv\nD8P7jp7HMLafu33Q949Ta32RVU4C7r4SWJnV+UV60/h/EemtlllSKscqQ+2zpAyVaQ5F8qTatK9J\n9ofo2ZCqrRmRdJrVtPffWZn1JCSlngQRkXjqSQjUs65I+oRxbGlsj0TH8v5xTzDTnuZQRHZO0p6+\nevVi1Gv/OEN9ClQREZEhLW58cVSAAMkTHaslUg6F1VZFim7OtDk8dvZjbD93e+TMSFH7J1mJOe39\nd5Z6EkREckA9CYF61hVx43+TihsvHNeTkLRHQkQkCfUkiIiI7IS4cb5jS2MjpyccWxobe5yonoGF\nxyyMPA5QtxlM1CNRm7jPaSh+fkOxTJJPChJEREQixDXiLzz+wsgu/wuPvzDR3OYQvQLs5s7NkeVJ\nutpq3JztRW5URjWw4z6nT9z4iSH3+en/VAaThhuJiOSAhhsF6l1XDCRxsff+X7j5C4kSlOuV0KzE\n6J6SJqI3WRPd3t1ne5afn/5PpR6G/BSoIiIiQ0G1QGDOtDmJ8gCi9j9j+RmR+8b1DCw8ZmHiqRej\nriHpCrN5F5eI3ntbWVSAANl+fvo/lcGk4UYiIlJYgzF8I+lKr0lnMIm7hjGlMYnOm3dJG9JN1hS5\nvZ6fX9L8gnqtGixSCwUJIiJSWHFPlweSJBwnLrehWs9AkqkX466hfJ4k582zpIno8w6bl+rn11+A\nmiTZvaj/p5IuBQkiIlJYgzF8o55zm0c1HOPKurlz86DOqT7UJU1E/96J30v186sWoMYFEBCd7F7U\n/1NJlxKXRURyQInLgaR1RSM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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2cfae940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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l17RWcx3bNjZxd4lmNpyB6FGJQpqfX9I73mmuGixDG06yAdV/d4dT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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c307becf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mdlf4+M3A+dmFIyKSD5WuuNzm7tE11kDkXJRm9j3gZGC9u78m3DaaoG/pJIKp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f59b3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QBbwP+EBGsYiweH5n5JoE5d17orr9zD1gvLoDiYxgac54EidpN4ek\nXYHizmF8+/jI2WpG0uBkkaSG+04P/h5V2h/S6ZKX9BpQKaloZEtPZuskmNlxwIUEU6Be6u4VO7xp\nnQSpt6TTmYo0kyJ3NyqXtKxoRJecei84VstCVyPx7rBINdLq3lfr9yerxeuSfKe1mJqISIEoSQgk\nLSsatShSGnf/4pKNuDnvDUs0j7xIHiT9Tidd9K3SDYRKNwSg+oHi9V5lutnHJIiIiGSuUesFpNHP\nO66fclrzyBdZXJ/0Zpy2shljaiZJv9NJv+uVxvRUGksQ9V2M27+0eN3g8RMb+zYmjmlXKEkQEZHC\nGknrBcRVBPq9f8ScQ9aiKtilu7+DF6/7xI2fqPuidrXE32wxNZuk3+mki75VSiqSDlCutD0qqWj0\nIohKEkREpLBG0oJccRWBUswj4RyyFFfBPuPHZ0TezV1297KmmGGmXLPMetPMkn6nky76Vin5TqsV\nI+kq7fW6IaAxCSIiOaAxCYE8lxVZzvOeB3EDVJNKe7xKEo0aQyOBWtaYSPIdreU7ncb4pmrLi6ym\nQBUREZEE8rJKclaS9ttutVb6vX/I9jS7diSt8KW9arBUlnRF76Tf0Vq+041cZVwtCSIiOaCWhIDK\nComTdKrLuBlm0mq5Ge4uctKpNJUsSrU0u5GIiIhIKK4/90XHXhTZJ/0bx3+jrmM9Ko0viBs/AWj8\niTSMWhJERHJALQkBlRVSSSNXqx1OpfEFcd2K0lzkT4pLYxJEREREyjSyP/dwKo0vSDplpkg9qLuR\niIiISINVms6ylvnwtciapE0tCSIiIiINNtzMNlEDlOPmwx88CLp8DEOztJzIyKMxCSIiOaAxCQGV\nFZIXScZPxM3cpDEMEkWzG4mIiIg0UFyXn1q6Ai2cvZC1Z65l+znbWXvm2ootAhrDIPWg7kYiIiIi\nCVSzhkGpy8+dj985YL2FenQF0iJrUg9qSRARERGpUtwaBmf8+IzIdQ+W3b0sdj2EtFQaBC1SKyUJ\nIiIiIlWKWwTt2b5nI/fv9/7I7Wl2BVo4e6EWWZPUqbuRiIiISJWSVu5brTUyUUi7K1AzrQEh+aCW\nBBEREZEqxVXuJ7RPiOzys+jwReoKJCOSkgQRERGRKsX1/7/o2Isiu/x84/hvqCuQjEjqbiQiIiJS\npeEWQYuq/KsrkIxEShJEREREElClX4pA3Y1ERERERGQAc/esY6iKmfUAQ1cKqc5EYEOK4YwEOudi\n0DkXx3DnfYC7T2pUMM1KZUVNinjeOudi0DlHq6q8GDFJwq4ws7vcfW7WcTSSzrkYdM7FUdTzbqSi\n/o2LeN4652LQOe8adTcSEREREZEBlCSIiIiIiMgARUkSlmUdQAZ0zsWgcy6Oop53IxX1b1zE89Y5\nF4POeRcUYkyCiIiIiIhUrygtCSIiIiIiUqVcJwlmdoyZrTGzh81sSdbx1IuZXWpm3Wb2x7Jt483s\nFjN7KHwcl2WMaTOz/c3sdjN7wMzuN7Mzwu25PW8zG21mvzOz+8Jz/ny4fYaZ/TY85++b2W5Zx5o2\nM2s1s1VmdkP4PNfnbGZrzWy1md1rZneF23L72W4GRSgvVFaorMjzdROKV1ZAfcuL3CYJZtYKfB04\nFngV8H4ze1W2UdXNZcAxg7YtAW5194OBW8PnebIN+JS7HwIcAfxd+P+b5/N+CTjK3V8LHAYcY2ZH\nAF8Cvhae8ybgoxnGWC9nAA+UPS/COb/N3Q8rm8ouz5/tTBWovLgMlRUqK/J93SxiWQF1Ki9ymyQA\nbwAedvdH3f1l4GrgpIxjqgt3/zmwcdDmk4DLw39fDixoaFB15u5Pufs94b+3EFwUppDj8/bA8+HT\ntvDHgaOAH4Tbc3XOAGY2FTgeuDh8buT8nGPk9rPdBApRXqisUFlBjq+bKisGSOXzneckYQrwRNnz\nJ8NtRfEKd38KgosksE/G8dSNmU0H5gC/JefnHTal3gt0A7cAjwC97r4t3CWPn/MLgX8CtofPJ5D/\nc3bgJ2Z2t5ktCrfl+rOdsSKXF4X5XKmsyP11s4hlBdSxvBiVUoDNyCK2aSqnnDGzPYFrgTPdfXNw\n4yC/3L0fOMzMOoDrgEOidmtsVPVjZu8Eut39bjN7a2lzxK65OefQPHdfb2b7ALeY2YNZB5RzRfhM\nFZrKCpUVodycc5m6lRd5bkl4Eti/7PlUYH1GsWThGTPbDyB87M44ntSZWRvBRf9Kd18ebs79eQO4\ney9wB0Ef2w4zKyX8efuczwNONLO1BF1AjiK4W5Tnc8bd14eP3QQF/BsoyGc7I0UuL3L/uVJZobIi\n3Cdv5wzUt7zIc5Lwe+DgcGT7bsD7gOszjqmRrgdODf99KvDDDGNJXdjX8BLgAXf/atlLuT1vM5sU\n3hXCzNqBtxP0r70deHe4W67O2d3Pcvep7j6d4Dt8m7svJMfnbGZ7mNlepX8DfwX8kRx/tptAkcuL\nXH+uVFaorCCn5wz1Ly9yvZiamR1HkEm2Ape6+9KMQ6oLM7sKeCswEXgGOAdYAVwDTAMeB05x98ED\n1kYsMzsS+AWwmp39Dz9L0Nc0l+dtZocSDEBqJUjwr3H3fzWzmQR3TsYDq4APuvtL2UVaH2ET8qfd\n/Z15Pufw3K4Ln44CvufuS81sAjn9bDeDIpQXKitUVpDT62a5opQVUP/yItdJgoiIiIiIJJfn7kYi\nIiIiIlIDJQkiIiIiIjKAkgQRERERERlASYKIiIiIiAygJEFERERERAZQkiAiIiIiIgMoSRARERER\nkQGUJIgkYGavN7M/mNnocKXD+83sNVnHJSIizUXlhYx0WkxNJCEz+wIwGmgHnnT38zIOSUREmpDK\nCxnJlCSIJGRmuwG/B14E/sLd+zMOSUREmpDKCxnJ1N1IJLnxwJ7AXgR3iERERKKovJARSy0JIgmZ\n2fXA1cAMYD93/2TGIYmISBNSeSEj2aisAxAZSczsb4Bt7v49M2sFfmVmR7n7bVnHJiIizUPlhYx0\nakkQEREREZEBNCZBREREREQGUJIgIiIiIiIDKEkQEREREZEBlCSIiIiIiMgAShJERERERGQAJQki\nIiIiIjKAkgQRERERERlASYKIiIiIiAzw/wHLvFtwbfmf1QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c29869eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5cuU8lzN3OmmrSjn7MUjjSJpulnSY2IG+n0nOGXGT0cWtn/QcE6em\n+ySY2XnAtH5BwvHu/rG41yjPVCqpWP5/XNrPYOY9EKmULAcJ+cpZVyQd573Jmujzvj2Wx11UpJk7\nX84AJa2Uqaz2Paj3FLVKK1f+f5xin69iQTOUHgzErX/pfZeW5Xtb6/MkrAYOzXs8AViTUllEmD1t\nUuwcBuWa90BE6ktcGkLcRFBRAQLE5xGnmVJQzpznpPMhlEs5h7QsR/pYNaSdolYPkqauxa0/mDkj\niqU6RX1Pkq5f7b4KqXRcBh4FJprZYUAX8D7gb1Iqi8iuPP+4kYpy8xxE0YzIIo0pacUb15IQd1Fx\nxWlXRN5FPHPimUU7XpZDI3TujXv/BurHMNDd3Nz7/dDzDxWkdlTi/5DUQBeVsvt/U2prS9z6EH2X\nv9jnq9IdlKv9vU1zCNQzgasIhkD9sbsX7VGkdCMRkXhKNwqUs66IS0MY1zKO3h29ifKFIfqiJeqi\ntVwpBVB8KMi0xowvpySpN5VOH6uGrKZYpaWc/WTKMdRpub63Nd0nYTAUJIiIxFOQEKhGn4SkF/0Q\nn3ccVbGX60JwoAuKrOW2J809j5PmBbkmiqtt1Zg0rRzfWwUJIiIZoiAhUO66ohwVcloTKemCslDS\nUWyq0ZJQ7PNVjoBTqq8eZrhWkCAikiEKEgK1WFckbRko193F8xecr9SUPOVMHyvHRdxALVVJW7FE\nSlXroxuJiIjUhEqPYJN0FJ6Zk2cy/+z5dIzpwDA6xnQMGCBEjXgztmVsov02urhRbK4+4+rI9/s7\nZ30n0f8hqWKdkJOOeiNSCWpJEBFpAGpJCCStK6rRgbfS+0h6hzzLqSm11A+jWAsToFYgqRi1JIiI\niAyg2B3bcknaMlBMVKtH3HCJL/W+VNE74fWolu7CF2thKuccECKDpZYEEZEGoJaEQNK6op6GlEw6\nhGdWOyjXi8H2SajkqDeSDaXWF2lNpiYiIpK6eppULK7Vo2VoCyObRyaa9EnSV8qkX4OdA6IWJn6T\n+qeWBBGRBqCWhEAt9kkol2KtHtfNuE53kTNMw91KEuqTICIiMoBy9heotGJ56rWUa59lcSNlVXoE\nrbh+KXHLRUqhdCMREcm0mZNn1sVF9RWnXRHZ6qG0ouorZaKzXMrPQ88/VDDfQiVSgeopbU7qh1oS\nRERE6kA9tXo0srh5KS6+++LIPiPzl8yv+AhacXNAKICUvaGWBBERkTpRL60ejSyuA3n/ZTl93he5\nvJypQKV0ghZJSkGCiIiISImSXtw3WVNkoFDuVCAFkFJuSjcSERERKVHcxf24lnGRKT+zjpulVCCp\nSwoSREREREoUl/9/9RlXR/YZ+c5Z31FfEqlLSjcSERERKdFA+f9RF/9KBZJ6pCBBREREJAFd9EsW\nKN1IREREREQKmPueU7zXIjPrBvacKaQ0+wPry1iceqBjzgYdc3YMdNwd7n5AtQpTq1RXDEoWj1vH\nnA065mgl1Rd1EyTsDTNb7O5T0y5HNemYs0HHnB1ZPe5qyup7nMXj1jFng4557yjdSERERERECihI\nEBERERGRAlkJEuanXYAU6JizQcecHVk97mrK6nucxePWMWeDjnkvZKJPgoiIiIiIlC4rLQkiIiIi\nIlKihg4SzOx0M1tuZs+Y2Zy0y1MpZvZjM1tnZv+Xt2ysmd1rZk+Hv/dLs4zlZmaHmtmvzOwpM3vS\nzC4OlzfscZvZCDP7XzN7IjzmL4bLDzOzR8JjvsnMhqVd1nIzsyYzW2pmvwgfN/Qxm9kKM1tmZo+b\n2eJwWcN+tmtBFuoL1RWqKxr5vAnZqyugsvVFwwYJZtYEfBs4AzgKeL+ZHZVuqSrmGuD0fsvmAPe5\n+0TgvvBxI9kBfNrdjwROBP4x/P828nFvBU5192OAY4HTzexE4F+Br4fH/DLwoRTLWCkXA0/lPc7C\nMb/V3Y/NG8qukT/bqcpQfXENqitUVzT2eTOLdQVUqL5o2CABOB54xt2fdfdtwI3AuSmXqSLc/TfA\nS/0WnwtcG/59LTC9qoWqMHdf6+6PhX9vJjgptNHAx+2BV8KHzeGPA6cCt4TLG+qYAcxsAnAW8MPw\nsdHgxxyjYT/bNSAT9YXqCtUVNPB5U3VFgbJ8vhs5SGgDVuU9Xh0uy4qD3H0tBCdJ4MCUy1MxZtYJ\nTAEeocGPO2xKfRxYB9wL/Anocfcd4SqN+Dm/CvgssDN8PI7GP2YH7jGzJWY2K1zW0J/tlGW5vsjM\n50p1RcOfN7NYV0AF64uhZSpgLbKIZRrKqcGY2b7ArcAn3H1TcOOgcbl7H3CsmbUCtwFHRq1W3VJV\njpm9E1jn7kvM7JTc4ohVG+aYQye7+xozOxC418z+kHaBGlwWPlOZprpCdUWoYY45T8Xqi0ZuSVgN\nHJr3eAKwJqWypOFFMzsEIPy9LuXylJ2ZNROc9K939wXh4oY/bgB37wEeIMixbTWzXMDfaJ/zk4Fz\nzGwFQQrIqQR3ixr5mHH3NeHvdQQV/PFk5LOdkizXFw3/uVJdoboiXKfRjhmobH3RyEHCo8DEsGf7\nMOB9wB0pl6ma7gAuDP++ELg9xbKUXZhr+CPgKXf/97ynGva4zeyA8K4QZtYCvI0gv/ZXwLvD1Rrq\nmN39Enef4O6dBN/h+919Jg18zGa2j5mNyv0NvAP4Pxr4s10DslxfNPTnSnWF6goa9Jih8vVFQ0+m\nZmZnEkSSTcCP3f2KlItUEWZ2A3AKsD/wInAZsBC4GWgHngfOc/f+Hdbqlpm9BfhvYBm78w8/T5Br\n2pDHbWZvIOiA1EQQ4N/s7v9iZocT3DkZCywFPuDuW9MraWWETcifcfd3NvIxh8d2W/hwKPAzd7/C\nzMbRoJ/tWpCF+kJ1heoKGvS8mS8rdQVUvr5o6CBBRERERESSa+R0IxERERERGQQFCSIiIiIiUkBB\ngoiIiIiIFFCQICIiIiIiBRQkiIiIiIhIAQUJIiIiIiJSQEGCiIiIiIgUUJAgkoCZvcnMfmdmI8KZ\nDp80s9enXS4REaktqi+k3mkyNZGEzOzLwAigBVjt7lemXCQREalBqi+knilIEEnIzIYBjwJ/Bk5y\n976UiyQiIjVI9YXUM6UbiSQ3FtgXGEVwh0hERCSK6gupW2pJEEnIzO4AbgQOAw5x94+mXCQREalB\nqi+kng1NuwAi9cTMLgB2uPvPzKwJeNjMTnX3+9Mum4iI1A7VF1Lv1JIgIiIiIiIF1CdBREREREQK\nKEgQEREREZECChJERERERKSAggQRERERESmgIEFERERERAooSBARERERkQIKEkREREREpICCBBER\nERERKfD/Af7UM44OL5znAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f521898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/DfhRhqGJiORCtZKE+pxpoqUlmE+9yDvaOuNnQiG6n/IhEXcF+wgrAhOnv7gG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\nEZFhlCSIiIiIiMgwShJERERERGSY/w9Cxj5aOHWFZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f442668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/u9K/k3G9Q0m3J5HWtLwjkbQHqFamWM2qJ+FvgDPd/X3h83cBr3L3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\nkQH+P53ZvCByMPlFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c28061630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MQkBlhYhIYcWWF5We3WgfYLu795pZK/D3wH8AdwD/SDDD0ZnALysZh0gjyXXF6f/1d3lh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\nB2auIeHPy+M9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c26879400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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imLTDKq/Jk+Gf/intKOqGOi4HVFaIiBRWbHlR6ZqE/YCrwn4JTcAN7n6Lmf0R+JmZfQNY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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2e3857f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EUqdUk61/jhqZvzrqTv/Ipoa8Bfi1v3+GHvcB26MK9opOo/jnP8NTT8F555X+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\nP3ti80S6dnYl8v3U+lS+xZY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c280c3518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wfkRWG8zsv8nSrcjdv1TGcEREEifXloT+nAdURZIQVYnvvS2ld4KQkm8/6A3t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\nRER6UJIgIiIiIiI9/H9DsUMeemuQbQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c299e04a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5uPDC0m+72rW2wp/+FHcUldXRETwmMEnY8X+7+4E8cN6NDOzexuCmBr580kGc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\nEZEelCSIiIiIiEgPShJERERERKSH/w/gc4Dso7a34wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f4183c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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q9PamsiUh87ud3dRCo/ex6JIv0PezYbw4cTQTx4xgNjA7+w3L4cUt29nnxa18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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f4ef128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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K2s4uRjQ3ccDuY9nzT4t54jd5lreWZ1Ccl+/9Oyd1dvVd/si18A/vKH39E07Y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\nYL8oYi9jgwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2d196cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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R0ou6Gn7+HefnbADPWTwn1lXV/ng18owJZzDn5DmMGTYGwxgzbAxz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c30f2cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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t7JZ/YsDgAQ3weq7DrtJ0dsL118M3vwkXXghf+AIM6T2RTr5pTppiNT9m9j9k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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2d986048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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eg/nzu77zv9z+XS5e8grrOzalHG0xoJZv77YL/O//Fraf3Xfv83POdzQkDbGa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\niEg3ChJERERERKQbBQkiIiIiItLN/wdMzxJ+YlQgmQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2d973c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LcXxHy1CtvN9RetvnUC7qbiRSBrm6QOU7NWquWZLiWvhNJGmy1ZIC\nkV1mIP8uOb2x682lx1+atYa0e4EoLapwH3VugxsH83r767vsHxWcFPMe9cb3tVSKCbJKJdtvIVdh\nuRLvdaGtGKVq9Yjzc6gktSSIVNDUCS08Omsy/7zsZB6dNTlnYT9qlqS5C5aVO5kiQnQt6fm/Oz9r\nwej8351fUK1qb6yNnD5+Oteeei1j9hqDYYzZa8yO+9lEFe6jzg2CoCNT/4b+O4KvfI+T6z0q5jlR\nLQ+9rUUi6v2O2l4qUb+FbF3HoHJBSyG/t1K2ehTzORT6XeoN373YggQzO8HMlpnZC2Y2K650iOQj\nqttPObsDRa0CHefq0CJJElXYzFYTDvB6++sFFU5z1UbGWUCYPn46L3/pZbZfvJ2Xv/Qy08dP59Lj\nLy2ocB91buvb12cNQqJqc4upsS30fY0qPH7+3s+XvStNoZ9zoZ9DqUT9FuqtPuv+6cJyOb/HhQaD\npQzKC/0c4gxodkcsA5fNrB74B/BB4BXgCeBMd3826jkajCblFrVKctRA5P/z7hbuXty6y/Y508aX\npDvQpMseoDVLQKCBzpKNBi4HSplX5BrEWwjD2H7xrjOeRQ3iHdI4hPZt7b1uUGQhXTVKNUC5p+NE\ndYEp5H1t7NOYNfCrt3o6vXOX7aUaZN3T4Neo97tUXWYKOU4xA9qByPODwmbKypbWs+adlTVNUb+3\nqHOI2r8n5fw9lHuAf775RVxBwnuAS9x9Snh/NoC7z4l6joIEKaeoQGDOtPHMXbAsa2G93ozOLL+f\nUhXic6VJYxKkOwUJgVLmFYUW4qMKm1EZe1QhsdDjFKucs9IUM/tLPuM/Mo8T9djZ7zqbm/96c97v\na6GKLVR2l6sgGDU2pJhAsZj3Nd/AK53WbN+jYoLgbK8dldZCfydxzqxVaIBS6oBml+P08tmNWoCV\nGfdfCbeJxCJX//+o7j3ZAgQoXXegqFmSFCCIVEZUl4IrT7wya5eZK0+8MrILQrZuF1H9/9e3r8+a\nnmL6eefqa1/O7gxR59bTYOPu6QEijxPVfeS+5+8r6H2N0lNXmt2Vq1tUqbrGlGpczUn7nxT53c7W\nPS3X+UV1y4t67ai0ptOQLU3ZxNVVCwofw5BreyW7IsbVknAGMMXdPxvePws4wt2/0G2/GcAMgNGj\nR797+fLsA2REdte+s+7N2pBqQHNTYywtCSKFSHJLQjnzilLMngLRtbbZjlWqGs9ctfm5aobjWK+g\nmHMutLa10JrtqBaJUnX7ynXOK9pWlKQmOeo1CpWrxaDcrx3FMG6ZdktBXbIqsaZDKVpuovYv1XdS\n3Y1ECpCr///MKeNiGZMgUogkBwmZemNeUWgBuFQLNVWiEFoqxXSvKOX7Ctn7yMfVJatUQVy5x9Xk\nUmh3ukKV8vdTynEepQgGiun2Vcj3It/8Iq51Ep4A9jezfYFW4OPAJ2JKi0hkIJC5jkG2Qc0TxwzO\ne90DEUmmQmfoSRdOdrcFI9frjt5rdNbCRjFdaUpRwComPVH99qO6j/T0vmZL8/Tx08s2WLyn9BRy\nbpD9c4h6XwsdV1PM9yLq/KLOLeq1o9JazLS52T7LXOtqZEt/ru9DrtfO7IqVNvaKsQXtf9a8s7K+\nbrmmnI2lJQHAzE4CrgDqgZ+6e85OYb2xdkhqS9TsRiLVQC0JgWLyinJ3QSj3gMliBkCXamBsqVo9\nij1OJbqPxKWQc4t6/3J1T4HCarZL+b6WoktOoTMxVWKWsXIPUC7VtaRXdzcqhoIEEZFoChICheYV\npSrkxvkaxRZySlHALmUAVMsF/nLraaakOFYlLkYc38lCu2Tl+m6Xe6rTUl1LFCSIiCSIgoRAoXlF\npaZFLOfc9rnmi48a2Fkq5Z6qsdrENWBWn8NOhRakCx1gnes9LfS14xo/oSBBRCRBFCQECs0rqqlw\nFfe6CtnEOfd8nArpLlPuWZIguZ9DlFJ01Sr2d1WKGdHK3XKjIEFEJEEUJAR6a0tCKfTGFZor0V2r\ntym0UFnulZtzpamWP4dSKsXUxdWkty+mJiIiErs4F1gqVNQMJuvb1xe0cFkpFbpoWi2ImsEmalrP\nbAEClHZGmiR+DqWUbUE4vadqSRARqQlqSQj0xtmNSqWaWj1qWaEDXSvRkiBSCLUkiIiI5CFbLWJv\nVE2tHrUsas2AIY1Dsn4+M949Q5+bVCUFCSIiIlVA3R96h6hg7coTr8z6+fz45B/rc5OqpO5GIiI1\nQN2NAsorpBKqpYuaSDb55hd9KpEYERERkVqRHtgqUsvU3UhERERERLqomu5GZvYakP+SeF0NBdaV\nMDnVQOecDDrn5OjpvMe4+7BKJaa3Ul5RlCSet845GXTO2eWVX1RNkLA7zGxR0vrq6pyTQeecHEk9\n70pK6nucxPPWOSeDznn3qLuRiIiIiIh0oSBBRERERES6SEqQcG3cCYiBzjkZdM7JkdTzrqSkvsdJ\nPG+dczLonHdDIsYkiIiIiIhI/pLSkiAiIiIiInmq6SDBzE4ws2Vm9oKZzYo7PeViZj81s7Vm9reM\nbYPN7I9m9nx4u3ecaSw1M3ubmT1oZs+Z2TNmdn64vWbP28z6mdnjZvbX8Jy/FW7f18weC8/5DjPb\nI+60lpqZ1ZvZEjP7bXi/ps/ZzF42s6Vm9pSZLQq31ex3uzdIQn6hvEJ5RS1fNyF5eQWUN7+o2SDB\nzOqBq4ETgYOAM83soHhTVTY3ASd02zYLuN/d9wfuD+/Xkm3AV9z9QOAo4N/Dz7eWz3srMNnd3wUc\nCpxgZkcB3wMuD8/5DeDcGNNYLucDz2XcT8I5H+fuh2ZMZVfL3+1YJSi/uAnlFcoravu6mcS8AsqU\nX9RskAAcAbzg7i+5+1vA7cBpMaepLNz9T8D6bptPA24O/78ZmFrRRJWZu6929yfD/zcSXBRaqOHz\n9sCm8G5D+OfAZOCucHtNnTOAmY0CTgauD+8bNX7OEWr2u90LJCK/UF6hvIIavm4qr+iiJN/vWg4S\nWoCVGfdfCbclxQh3Xw3BRRIYHnN6ysbMxgITgMeo8fMOm1KfAtYCfwReBFLuvi3cpRa/51cAFwDb\nw/tDqP1zduAPZrbYzGaE22r6ux2zJOcXifleKa+o+etmEvMKKGN+0adECeyNLMs2TeVUY8xsAHA3\n8CV33xBUHNQud+8EDjWzJuBXwIHZdqtsqsrHzE4B1rr7YjN7f3pzll1r5pxDk9x9lZkNB/5oZn+P\nO0E1LgnfqURTXqG8IlQz55yhbPlFLbckvAK8LeP+KGBVTGmJw6tmNhIgvF0bc3pKzswaCC76t7r7\nvHBzzZ83gLungIcI+tg2mVk64K+17/kk4MNm9jJBF5DJBLVFtXzOuPuq8HYtQQZ/BAn5bsckyflF\nzX+vlFcorwj3qbVzBsqbX9RykPAEsH84sn0P4OPAPTGnqZLuAc4O/z8b+HWMaSm5sK/hDcBz7v7D\njIdq9rzNbFhYK4SZNQIfIOhf+yBwerhbTZ2zu89291HuPpbgN/yAu0+nhs/ZzPY0s4Hp/4EPAX+j\nhr/bvUCS84ua/l4pr1BeQY2eM5Q/v6jpxdTM7CSCSLIe+Km7XxpzksrCzG4D3g8MBV4FLgbmA3cC\no4EVwBnu3n3AWtUys2OAR4Cl7Ox/+HWCvqY1ed5mdgjBAKR6ggD/Tnf/tpm9naDmZDCwBPiku2+N\nL6XlETYhf9XdT6nlcw7P7Vfh3T7AL9z9UjMbQo1+t3uDJOQXyiuUV1Cj181MSckroPz5RU0HCSIi\nIiIiUrha7m4kIiIiIiJFUJAgIiIiIiJdKEgQEREREZEuFCSIiIiIiEgXChJERERERKQLBQkiIiIi\nItKFggQREREREelCQYJIAczscDN72sz6hSsdPmNmB8edLhER6V2UX0i102JqIgUys+8A/YBG4BV3\nnxNzkkREpBdSfiHVTEGCSIHMbA/gCWALcLS7d8acJBER6YWUX0g1U3cjkcINBgYAAwlqiERERLJR\nfiFVSy0JIgUys3uA24F9gZHufl7MSRIRkV5I+YVUsz5xJ0CkmpjZp4Bt7v4LM6sH/mxmk939gbjT\nJiIivYfyC6l2akkQEREREZEuNCZBRERERES6UJAgIiIiIiJdKEgQEREREZEuFCSIiIiIiEgXChJE\nRERERKQLBQkiIiIiItKFggQREREREelCQYKIiIiIiHTx/wHI9CCkzV+qzgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f52bb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wDjgY2Dfbbtmea2azzGyxmS1+5ZVXyllMkZqRzs8fvukN1gweunV7c6qJVFNjr31TTY3s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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f47ff98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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m1BgxAp56KulSVF9HR3rHJEDQk7BuHfzyl8FdnoDL7FWuf2o5GzZu3rLaDv0a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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f3335c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QEUmifO9u9OFcr5vZKe5e87emi6rAq7ohMH8+DB0K7353ebZfrZI663Iqlewx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\nXwzAN5iuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f4c28d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0vtDAZZGM/faDG28MehYee6zwn5Ur4SMfgYULYd06Wm65kUPP+TIj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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2e29c908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Vh8cfDyqOaRmPkNHSks4kQS0JsHIlPPUUDBkCwB51q1nW+eZmqzaPGBy7tWnq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\nSYKIiIiIiPTw/wHVD3cHdNGbIQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2f4260b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MOH5PmrcdgpnRvO0QZhy/Jxccs3usc0eldeqR7wrujx0bXGxLS4KvtPQXyitEREqv7AOX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c30f64be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MVm7atKnUoYoMCqn++SN27mDr0L17ltfX1VJXW91r3braakbvVZt1O/mYOa2RBbOm0lhf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\nAH0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c300fda20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xi = x # initialization of input\n",
    "yi = y # initialization of target\n",
    "# x,y --> use where no need to change original y\n",
    "ei = 0 # initialization of error\n",
    "n = len(yi)  # number of rows\n",
    "predf = 0 # initial prediction 0\n",
    "\n",
    "for i in range(30): # loop will make 30 trees (n_estimators). \n",
    "    tree = DecisionTree(xi,yi) # DecisionTree scratch code can be found in shared github/kaggle link. \n",
    "                               # It just create a single decision tree with provided min. sample leaf\n",
    "    tree.find_better_split(0)  # For selected input variable, this splits (<n and >n) data so that std. deviation of \n",
    "                               # target variable in both splits is minimum as compared to all other splits\n",
    "    \n",
    "    r = np.where(xi == tree.split)[0][0]   #  finds index where this best split occurs\n",
    "    \n",
    "    left_idx = np.where(xi <= tree.split)[0] # index lhs of split\n",
    "    right_idx = np.where(xi > tree.split)[0] # index rhs of split\n",
    "    \n",
    "    predi = np.zeros(n)\n",
    "    np.put(predi, left_idx, np.repeat(np.mean(yi[left_idx]), r))  # replace left side mean y\n",
    "    np.put(predi, right_idx, np.repeat(np.mean(yi[right_idx]), n-r))  # right side mean y\n",
    "    \n",
    "    predi = predi[:,None]  # make long vector (nx1) in compatible with y\n",
    "    predf = predf + predi  # final prediction will be previous prediction value + new prediction of residual\n",
    "    \n",
    "    ei = y - predf  # needed originl y here as residual always from original y    \n",
    "    yi = ei # update yi as residual to reloop\n",
    "    \n",
    "    \n",
    "    # plotting after prediction\n",
    "    xa = np.array(x.x) # column name of x is x \n",
    "    order = np.argsort(xa)\n",
    "    xs = np.array(xa)[order]\n",
    "    ys = np.array(predf)[order]\n",
    "    \n",
    "    #epreds = np.array(epred[:,None])[order]\n",
    "\n",
    "    f, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize = (13,2.5))\n",
    "\n",
    "    ax1.plot(x,y, 'o')\n",
    "    ax1.plot(xs, ys, 'r')\n",
    "    ax1.set_title(f'Prediction (Iteration {i+1})')\n",
    "    ax1.set_xlabel('x')\n",
    "    ax1.set_ylabel('y / y_pred')\n",
    "\n",
    "    ax2.plot(x, ei, 'go')\n",
    "    ax2.set_title(f'Residuals vs. x (Iteration {i+1})')\n",
    "    ax2.set_xlabel('x')\n",
    "    ax2.set_ylabel('Residuals')\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Errors are not changing much after `20th iteration` and pattern in residuals is also removed. Residuals look distributed around the mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maths behind this logic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ Predictions = y_i^p $  \n",
    "$ Loss = L(y_i, y_i^p) $  \n",
    "$ Loss = MSE = \\sum {(y_i - y_i^p)}^2 $  \n",
    "$ y_i^p = y_i^p + \\alpha * \\delta {L(y_i, y_i^p)}/ \\delta{y_i^p } $  \n",
    "$ y_i^p = y_i^p + \\alpha * \\delta {\\sum {(y_i - y_i^p)}^2}/ \\delta{y_i^p } $  \n",
    "which becomes, $ y_i^p = y_i^p - \\alpha * 2*{\\sum {(y_i - y_i^p)}} $  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where, $y_i$ = ith target value, $y_i^p$ = ith prediction, $ L(y_i, y_i^p) $ is Loss function, $\\alpha$ is learning rate. So the last equation tells us that, we need to adjust predictions based on our residuals, i.e. $\\sum {(y_i - y_i^p)}$. This is what we did, we adjusted our predictions using the fit on residuals. (accordingly adjusting value of $\\alpha$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ Loss = MSE = \\sum {(y_i - y_i^p)}^2 $  \n",
    "\n",
    "where, $y_i$ = ith target value, $y_i^p$ = ith prediction, $ L(y_i, y_i^p) $ is Loss function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ y_i^p = y_i^p + \\alpha * \\delta {\\sum {(y_i - y_i^p)}^2}/ \\delta{y_i^p } $  \n",
    "which becomes, $ y_i^p = y_i^p - \\alpha * 2*{\\sum {(y_i - y_i^p)}} $  \n",
    "\n",
    "where, $ \\alpha $ is learning rate and $ {\\sum {(y_i - y_i^p)}} $ is sum of residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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